where \(\xi \in \mathbb {Q}_{p}\) . This Fourier transform can be extended to \(L^{2}(\mathbb {Q}_{p})\)  and we have the Parseval theorem [1]} as follows
\(\langle f,g \rangle = \langle \hat{f}, \hat{g} \rangle , \hspace{28.45274pt} \forall ~ f, g \in L^{2}(\mathbb {Q}_{p}).\) 
